2 Answers
2

Not quite. There are a lot of (somewhat competing) theories on meter, etc., and it may be impossible to distinguish one meter from another aurally in certain circumstances. However, one feature common to meters is the allusion that the downbeat (that is, the beat occurring immediately following the bar line) is the strongest beat of the measure. So, in the first of your examples, the notes occurring with the text "Once" and "swag" would be considered (for what it's worth) the strongest beats of each measure, while in your second example, "Once" would be considered stronger than "swag."

Now, my explanation of the first example did not preclude "Once" from being stronger than "swag"; in fact, there is no direct comparison at all. Theorists have a name for the phenomenon in which multiple measures add up to a larger unit, or "hypermeasure," in which some of the metric conventions that apply to measures apply to groups of measures as well. I would link to Wikipedia, but I find its current description of the phenomenon defective. A somewhat simplified definition is on the Indiana University School of Music website. One could certainly argue that the second measure of your first example constitutes the second hyperbeat of the first hypermeasure of your piece, in which case there may be no actual difference in metric stress between the two examples.

There are, as Andrew says, many subtleties inherent in metering. Chief among them, in general terms, is the "feel" that the meter generally implies.

For instance, in your example, if the top edit were metered in 2/2, it would feel much the same as the bottom edit. The difference is that the emphasis inherent in the beats of each time signature falls on different syllables in the music.

"1" is almost always the most important beat of any measure. Then, in meters that are divisible by 2, the beat that starts the second half of the measure (3 for 4/4, 4 for 6/8) is the next most emphatic. Other beats are usually less emphasized.

So, as written, your first edit would be emphasized something like:

ONCE a JOL-ly SWAG-MAN...

while your second one would be emphasized a bit more naturally:

ONCE a jol-ly SWAG-man...

if the first edit were in 2/2, it would usually be taken at a faster clip (up to twice as fast as you'd take it in 4/4), but the emphasis would remain much the same as in the first. However, a conductor, at his discretion, can instruct his group however he likes; He may tell them to de-emphasize the "2" of a 2/2-metered piece and you'd end up with something very close to the second edit in overall feel, but using fewer "flags" on the notes making the music "cleaner" and easier to read.